Averaged reflected EDSs with jumps and McKean-Vlasov type retrograde EDSs: theoretical and numerical study.

Summary This thesis is devoted to the theoretical and numerical study of two main research topics: mean-reflected stochastic differential equations (SDEs) with jumps and backward stochastic differential equations (SRDEs) of the McKean-Vlasov type.The first work of my thesis establishes the propagation of chaos for mean-reflected SDEs with jumps. We first studied the existence and uniqueness of a solution. We then developed a numerical scheme via the particle system. Finally we obtained a convergence speed for this scheme.The second work of my thesis consists in studying the McKean-Vlasov type EDSRs. We have proved the existence and uniqueness of solutions of such equations, and we have proposed a numerical approximation based on the Wiener chaos decomposition as well as its convergence speed.The third work of my thesis is interested in another type of simulation for McKean-Vlasov type EDSRs. We have proposed a numerical scheme based on the approximation of the Brownian motion by a random walk and we have obtained a convergence speed for this scheme.Moreover, some numerical examples in these three works allow to notice the efficiency of our schemes and the convergence speeds announced by the theoretical results.